LatentFlow: Componentwise Nonlinear Continuation for Multivariate Time-Series Forecasting

Multivariate forecasting architectures increasingly expose structure through decomposition, temporal scales, spectral routing, or variable-aware representations. Yet a distinct design question remains less directly isolated: once several structured temporal coordinates are available, when should their coordinate axis be reduced relative to the nonlinear forecasting operator? We study this representation–continuation interface with LATENTFLOW, an architecture for componentwise nonlinear continuation. A prefix-only encoder constructs structured coordinates, and shared coordinate-modulated variate–patch operators transform each coordinate separately through horizon projection and decoding; only the resulting future forecasts are then aggregated. A complementary linear bank handles simple extrapolative behavior. Under a controlled fixed-budget protocol with 2,048 matched training windows per task, LATENTFLOW achieves the lowest aggregate MSE and MAE among seven evaluated implementations, wins 23 of 28 seed-matched MSE comparisons against TimePro, and retains a 1.38% mean task-wise MSE advantage across five seeds. More importantly, a matched intervention that reduces the same coordinate axis before nonlinear continuation increases mean relative MSE by 5.12% (95% source–seed clustered interval [2.42, 8.44]%). Conversely, replacing the GP-derived coordinates with a matched deterministic multibranch representation yields nearly identical aggregate point-forecasting error and an even 14–14 task split. Together, these results show that the main effect is not tied to a particular stochastic parameterization, but to the computation that consumes the representation: structured coordinates can be more effective when they remain computationally explicit through nonlinear continuation and are fused only after their futures are formed.